ST workshop 2008

1

ST workshop 2008

Conception of LHCD Experiments on the Spherical Tokamak Globus-M

O.N. Shcherbinin, V.V. Dyachenko, M.A. Irzak,S.A. Khitrov

A.F.Ioffe Physico-Technical Institute, St.Petersburg, Russia

2

Outline

1. Specific features of LHCD experiments on spherical tokamaks.

2. Ray tracing in spherical tokamaks.

3. Full-wave 2D modeling of wave propagation in the Globus-M.

4. Simulation of the GRILL antenna. Spectra. Wave reflection.

5. Design of the LHCD system for the Globus-M.

3

The Main Problems in LHCD Experiments on Spherical Tokamaks

In conventional tokamaks:

ωpe ≈ ωBe

N||cr  1.5–1.8

In spherical tokamaks:

ωpe » ωBe

N||cr  7–10

1.for such high N|| the coupling efficiency

is very poor and 2.RF energy is absorbed at the periphery

4

The New Approach in LHCD Experiments on Spherical Tokamaks

In spherical tokamaks the strong poloidal inhomogeneity of the magnetic field (due to low aspect ratio and high

elongation) allows a new approach:

1. Waves with comparatively low N|| (3–5) should be

excited in poloidal rather than toroidal direction.

2. Waves propagate at first at the plasma periphery, their N|| is increased due to the poloidal

inhomogeneity, and finally they penetrate into the dense plasma.

3. Absorption of the waves takes place in the vicinity of poloidal resonance by Landau damping on electrons.

5

Experimental Set-up for LHCD in Globus-M

R=0.36 m, a=0.24 m, B0=0.4 T, Ip=0.25 MA, vertical elongation – 1.6, triangularity – 4 cm, n0=4·1013cm-3,

nb=1·1011cm-3, Te0=400eV

f=2450 MHz

x

yz

x

y

z

R

Bpol

Ipl , B0

6

Poloidal Resonances

-20 -10 0 10 20

x, cm

-40

-30

-20

-10

0

10

20

30

40

y, c

m

-20 -10 0 10 20

x, cm

-40

-30

-20

-10

0

10

20

30

40

Ip=250 kA f=2450 MHz f=3000 MHz

0

0

2

2

2

2

B

B

r

B

B

N 

In 2D geometry 2 conditions are necessary:

1.

2.

-20 -10 0 10 20

-40

-30

-20

-10

0

10

20

30

40

Ip=210 kAf=2450 MHz

(blue curves)

(red ovals)

7

Ray Trajectory at Ntor0= 0, Npol0= -3.78

Red lines – ray trajectory, blue line – Npar ,

green line – wave absorption

0

30

60

90

120

150

180

210

240

270

300

330

R ay position vs toro ida l angle

0 0.2 0.4 0.6 0.8 1

rho

-30 -25 -20 -15 -10 -5 0 5 10 15 20

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

35

40

45

R ay pro jection on the po lo idal cross-section

0.0 5.0 10.0 15.0 20.0 25.0path

-12.0

-8.0

-4.0

0.0

Np

ar

0

0.5

1

rho,

Ka

bs

a) b)

c)

x, cm

8

Ray Trajectory at Starting Stage

1. Ray is allowed to propagate in one poloidal direction only.

2. Ray starts in a kind of plasma waveguide, between conversion layer and critical density.

3. Ray turns gradually in toroidal direction and runs against plasma current.

“Projection on the wall”Projection on the poloidal cross-section

1 5 2 0x, cm

-10

-5

0

5

y, c

m

-120 -90 -60 -30 0

to ro ida l angle , deg.

-60

-30

0

polo

idal

ang

le

, deg

.

9

Ray Trajectory at Ntor0= 0, Npol0= -3.8

Red lines – ray trajectory, blue line – Npar ,

green line – wave absorption

0

30

60

90

120

150

180

210

240

270

300

330

R ay position (rho)vs toro ida l ang le

0 0.2 0.4 0.6 0.8 1

rho

-30 -25 -20 -15 -10 -5 0 5 10 15 20x, cm

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

35

40

45

y, c

m

R ay pro jection on thepolo ida l cross-section

0.0 10.0 20.0 30.0 40.0path

-16.0

-8.0

0.0

Npa

r

0

0.5

1

rho,

Kab

s

10

Full absorption position (in rho units)

in the range of Npol0= -3.3 – -4.1

3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1-N pol0

0.2

0.4

0.6

0.8

1

End

of r

ay (

rho)

N tor0= 0 .0 , 0.2

This range of Npol corresponds roughly to excited wave

spectra (calculated)

11

Simulation by Full-Wave 2D Code

Simplifying assumptions: 1. The dimensions of the installation and plasma current value were diminished by 2 times2. The shape of magnetic flux surfaces was calculated by formula, but not by equilibrium code 3. The electric fields at the antenna output were taken not self-

consistent with plasma response

-15 -10 -5 0 5 10 15

Npol

E

y

rel.u

n.

The external field spectrum, created by

the grill antenna:8 waveguides,

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Comparison of Full-Wave Modeling and Ray-Tracing Result

8 waveguides with

Black “islands” – Landau damping regions

Npol03.8

-10 -5 0 5 10

-20

-15

-10

-5

0

5

10

15

20

-40

-36

-32

-28

-2

-1

-0 .8

-0 .6

-0 .4

-0 .2

0

0 .2

0 .4

0 .6

0 .8

1

2

28

x, cm

y, c

m

-15 -10 -5 0 5 10x, cm

-20

-15

-10

-5

0

5

10

15

20

y, c

m

RF field distribution

13

Excitation of Fields with Opposite Phasing

-10 -5 0 5 10

-20

-15

-10

-5

0

5

10

15

20

-1.4

-0.5

-0.4

-0.3

-0.2

-0.1

-0.05

0

0.05

0.1

0.2

0.3

0.4

1.2

-15 -10 -5 0 5 10x, cm

-20

-15

-10

-5

0

5

10

15

20

y, c

m

8 waveguides with Npol0= - 11.4

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RF Energy Deposition Profiles

1. Waves propagate in -direction only.

2. At opposite phasing the wave excitation is determined by additional (smaller) peak in the external field spectrum.

0 0.2 0.4 0.6 0.8 1

0

1

2

3

4P

abs,

rel

.un.

8 waveguides

Solid line -

Dashed line -

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Self-consistent Grill Modeling

1. The surface impedance matrix was found by solving the problem of wave propagation in a 1D plasma slab with parameters

corresponding to the Globus-M equatorial plane. 2. The waves entering the plasma were assumed to be absorbed in

the plasma depth.

3. The impedance matrix played the role of boundary condition for 3D simulation of antenna operation.

4. The basic configuration of grill includes 12 waveguides of 8.5 mm height, stacked vertically, one atop the other. No multi-junction

scheme was used. 5. Higher reflected modes in waveguides were taken into account to

obtain self-consistent solution.

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Grill Modeling. Wave Spectra.

- 5 0 5 1 0 1 5 2 0 2 5 3 0 3 5

-N pol

0

0.1

0.2

0.3

Px(

Npo

l)

43 .1%

40.6%

12.6%

Krefl=25%

Krefl=44%

- 5 0 5 1 0 1 5 2 0 2 5 3 0 3 5

-N pol

0

0.1

0.2

0.3

Px(

Npo

l)

12%

68%

18%

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2D Wave Spectra

-4 -2 0 2 4

N tor

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

Np

ol

-4 -2 0 2 4

N tor

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

Npo

l

Solid blue line – magnetic field direction

19

Waveguide Phasing

Optimal range of phasing – 90 - 120 degrees.

Coefficients of total reflection at change of phasing

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Change of Spectra at Grill Tilting.

Δα=+12° Δα=+8° Δα=−8°

1st peak 17% 34% 43% 50%

2nd peak 80% 60% 41% 24%

-4 -2 0 2 4

Ntor

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

-4 -2 0 2 4

Ntor

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

-4 -2 0 2 4

Ntor

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

-4 -2 0 2 4

Ntor

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

Npo

l

Solid blue line – magnetic field direction, red – waveguide broad side direction

21

Ray Trajectory at Ntor0= -1.5, Npol0= -17.8

0

30

60

90

120

150

180

210

240

270

300

330

R ay position (rho)vs toro ida l angle

0 0.2 0.4 0.6 0.8 1

rho

-30 -25 -20 -15 -10 -5 0 5 10 15 20x, cm

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

35

40

45y,

cm

R ay pro jection on thepolo ida l cross-section

0.0 5.0 10.0 15.0 20.0 25.0path

-12.0

-8 .0

-4 .0N

par

0

0.5

1

rho

, Kab

s

22

RF System Set-up

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Conclusions1. It was found that there exists a rather wide range of experimental

condition when LH waves excited by a grill in poloidal direction propagate in peripheral plasma layer, turn gradually in toroidal direction and enter the bulk plasma. The allowed direction of poloidal propagation is determined by direction of toroidal magnetic field. The waves propagate toroidally against plasma current that is favorable for current drive perspective.

2. The absorption of the waves in present experimental condition in Globus-M takes place at ρ = 0.6 – 0.8. At higher plasma current the absorption region shifts to ρ ≈ 0.4.

3. The lowest reflection coefficients in grill operation are 20% – 25%. At later stages the multi-junction scheme will be used, which will enhance the efficiency of the antenna operation.

4.The starting stage, when the waves propagate in peripheral plasma layer, is the most dangerous for success of experiments. It is difficult now to evaluate parasite wave absorption in this stage and role of vessel walls in the process. The classical collisions do not seem to be dangerous in this respect.

The work was supported by the RFBR grant 07-02-13583.

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Wave Spectra at out-phase excitation

- 5 0 5 1 0 1 5 2 0 2 5 3 0

-N pol

0

0.04

0.08

0.12

0.16

0.2

Px(

Npo

l)

-4 -2 0 2 4

Ntor

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

Np

ol

6 waveguides of 17 mm height

Krefl=34%

9%

24.4%

44%

20%

25

Globus-M characteristics

Parameter Designed Achieved

Toroidal magneticfield 0.62 T 0.55 TPlasma current 0.5 MA 0.36 MAMajor radius 0.36 m 0.36 mMinor radius 0.24 m 0.24 mAspect ratio 1.5 1.5Vertical elongation2.2 2.0Triangularity 0.3 0.45Average density 11020 m-3 0.71020 m-

3

Pulse duration 0.2 s 0.085 sSafety factor, edge4.5 2Toroidal beta 25% ~10% OH

ICRF power 1.0 MW 0.5 MW Frequency 8 -30 MHz 7–30 MHZ Duration 30 mc 30 mc

NBI power 1.0 MW 0.7 Mw Energy 30 keV 30 keV Duration 30 mc 30 mc